International Journal of Partial Differential Equations and Applications
ISSN (Print): 2376-9548 ISSN (Online): 2376-9556 Website: http://www.sciepub.com/journal/ijpdea Editor-in-chief: Mahammad Nurmammadov
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International Journal of Partial Differential Equations and Applications. 2016, 4(1), 7-15
DOI: 10.12691/ijpdea-4-1-2
Open AccessArticle

Harmonic Oscillations and Resonances in 3-D Nonlinear Dynamical System

Usama H. Hegazy1, and Mousa A. ALshawish1

1Department of Mathematics, Faculty of Science, Al-Azhar University, Gaza, Palestine

Pub. Date: July 20, 2016

Cite this paper:
Usama H. Hegazy and Mousa A. ALshawish. Harmonic Oscillations and Resonances in 3-D Nonlinear Dynamical System. International Journal of Partial Differential Equations and Applications. 2016; 4(1):7-15. doi: 10.12691/ijpdea-4-1-2

Abstract

This paper is concerned with the three dimensional motion of a nonlinear dynamical system. The motion is described by nonlinear partial differential equation, which is converted by Galerkin method to three dimensional ordinary differential equations. The three dimensional differential equations, under the influence of external forces, are solved analytically and numerically by the multiple time scales perturbation technique and the Runge-Kutta fourth order method. Phase plane technique and frequency response equations are used to investigate the stability of the system and the effects of the parameters of the system, respectively.

Keywords:
Galerkin method resonances nonlinearities

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